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Tucker Ortiz

08/27/2024 · Senior High School

The box plots summarize the masses, in kilograms, of two groups of gazelles. Based on the box plots, which of the following statements must be true?

A. The mean mass of group 1 is greater than the mean mass of group 2. B. The mean mass of group 1 is less than the mean mass of group 2. C. The median mass of group 1 is greater than the median mass of group 2. D. The median mass of group 1 is less than the median mass of group 2.

Answer
expertExpert-Verified Answer

Ortiz Ramos
Specialized Tutor
5.0 (34votes)

C. The median mass of group 1 is greater than the median mass of group 2.

Solution

  • The box plot shows the median as the line inside the box.
  • For Group 1, the median is around 26 kilograms.
  • For Group 2, the median is around 24 kilograms.
  • Therefore, the median mass of Group 1 is greater than the median mass of Group 2.

 

Supplemental Knowledge

Box plots, also known as box-and-whisker plots, are a graphical representation of data that show the distribution through their quartiles. They provide a visual summary of the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum values in a data set.

  1. Median:
    • The middle value of a data set when it is ordered from least to greatest.
    • Represented by the line inside the box in a box plot.
  2. Quartiles:
    • Q1 (First Quartile): The median of the lower half of the data.
    • Q3 (Third Quartile): The median of the upper half of the data.
  3. Interquartile Range (IQR):
    • The range between Q1 and Q3.
    • Indicates where the middle 50% of data lies.
  4. Whiskers:
    • Lines extending from the box to the minimum and maximum values within 1.5 times the IQR from Q1 and Q3, respectively.

 

Practical Insights 

Box plots have long been employed in fields including finance, biology and social sciences to compare distributions across groups or datasets. Box plots make this task simple by visualizing data like test score comparison between classes or weight distribution among species effectively.

 

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